Robust Inference for an Interval-Monitored Step-Stress Experiment under Proportional Hazards

Abstract

Accelerated life tests (ALTs) are widely used in reliability analysis to infer on product lifetimes under normal operating conditions from data collected at higher stress levels. In step-stress ALTs, the stress is increased at predetermined times and kept constant between changes, accelerating failures and reducing test duration and cost. While many ALT studies assume a specific lifetime distribution, some applications require a more flexible formulation satisfying the proportional hazards (PH) assumption, under which stress acts multiplicatively on the hazard rate. In this paper, we study step-stress ALTs under a PH framework with linear and quadratic baseline hazard functions. We focus on settings where continuous monitoring is impractical and failures are observed only at scheduled inspections, yielding interval-censored count data. To achieve robustness and efficiency in this context, we introduce a family of minimum density power divergence estimators (MDPDEs) for model parameters, device reliability, and lifetime measures such as the mean lifetime and distributional quantiles. We derive the corresponding asymptotic distributions and construct approximate confidence intervals. Monte Carlo simulations assess the estimators' efficiency and robustness, and real-data examples illustrate the practical value of the proposed model and inferential methods.